X-ray spectral analysis



Jan. 8, 1963 J. LADELL ETAL 3,072,789

X-RAY SPECTRAL ANALYSIS Filed June 15. 1960 3 Sheets-Sheet 1 AXIS OFROTATION INVENTORS. efofiuvA LADEZL y NATHAN/SPIHBERG.

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X-RAY SPECTRAL ANALYSIS 3 Sheets-Sheet 2 Filed June 13, 1960 INVENTORS.

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United States PatentOfilice 3,072,789 Patented Jan. 8, 1963 1 3,072,789X-RAY SPECTRAL ANALYSES Joshua Ladeil, Flushing, and Nathan Spielberg,Hartsdale, N.Y., assignors to North American Philips Company, Inc, NewYork, Niifl, a corporation of Delaware Filed June 13, 1960, Ser. No.35,635 6 Ciaims. (Cl. 250-515) Our invention relates to analysis ofmaterials by X-rays and in particular to a method and apparatus for thespectrochemical analysis of materials by X-rays.

in apparatus for fluorescent X-ray chemical analysis, it is desirablethat the recorded spectra be as simple as possible, consistent with thespectrum of the specimen being analyzed. Unfortunately, however, thedispersing crystals employed inevitably contain numerous sets ofcrystallographic planes, and these give rise to extra reflections, themost commonly recognized of which are the higher order of reflectionsarising from planes whose normals are colinear with the normal to theprincipal planes. In addition to these, however, there may bereflections from planes Whose normals are slightly tilted with respectto the normal to the principal diffracting planes.

Extra reflections due to planes with tilted normals give rise topossible misidentification of the observed spectra, or if correctlyidentified, lead to spectral interferences which raise the minimumdetectable limit of the instrument.

It is a principal object of our invention to substantially eliminateextra reflections due to planes with tilted normals from the dispersingcrystal used in X-ray spectrochemical analysis and thereby improve therecorded spectra from a specimen being analyzed by X-rays.

It is a further object of our invention to simplify the identificationof the observed spectra of a spectrochemical analysis by suppressing oreliminating extra reflections.

It is a still further object of our invention to increase thesensitivity of a conventional X-ray spectrograph.

It is another object of our invention to permit increase of the relativeintensity of principal reflections from the analyzing crystal of anX-ray spectrograph through the use of larger angular divergenceparameters but with the suppression or elimination of extra reflectionswhich will indirectly occur and which would lead to spectralinterferences.

These and further objects of our invention will appear as thespecification progresses.

In accordance with our invention, We have found that extrareflectionsdue to planes with tilted normals can be suppressed or eliminated bychoice of the reflecting crystal, proper orientation of the reflectingcrystal, or by appropriate collimation in the lateral plane, or anycombination of these features.

The invention will be described in connection with the accompanyingdrawing in which:

FIGS. la and lb show, respectively, an elevational (equatorial plane ofdiffraction) and a plan (lateral plane of diffraction) view of an X-rayspectrograph and its geometry;

FIG. 2 shows schematically the detecting volume in the equatorial planeof the spectrograph;

'FIG. 3a shows schematically the detecting volume in the lateral plane;

FIG. 3b shows the locus of the center of the detecting volume in theequatorial plane; and

FIGS. 4a, 4b, 4c and 4d show recorded spectra obtained with aspectograph using the invention compared with a spectograph not usingthe'invention.

In FIG. 1, X-rays generated by an X-ray tube 1 are incident upon aspecimen 2 and generate characteristic fluorescent X-rays from anelement within the specimen whose absorption edge is longer than theshortest wavelength of X-rays incident upon the specimen. Thefiuorescent X-rays are incident upon a crystal 3 adapted to rotate aboutan axis 0. X-rays of diiferent Wave-lengths are reflected at differentangles by the crystal 3, some of which enter a detector 4 mounted forrotation on a circular are 5, at twice the angular speed of rotation ofcrystal 3. Divergence limiting slits 6 are provided between the specimenand the crystal as well as divergence limiting slits 7 between thecrystal and the detector.

The reason for the appearances of lines which are attributable to extrareflections due to planes with tilted normals can best be understoodfrom a consideration of the geometry of the instrument as shown in FIGS.1a and lb, and the following explanation. crystal on the crystal at O isdiffracted in a direction unit vector s making an angle Y with s thusY=cos- (s.s (1) Because of the extended size of the source and crystal,

the rays incident on the crystal can deviate from s up to a maximumamount of i /z 0: in the equatorial plane and up to a maximum amount of1 /25 in the lateral plane of incidence' Similarly, because of theextended size of the crystal and detector, the rays scattered into thedetector can deviate by a maximum amount i /za in the equatorial planeand 1 /2/8 in the lateral plane of diffraction. 0: 0: 8 and 9 arecontrolled by the limiting slits 6 and 7 shown in FIGS. 1a and 1b.

In order to show what occurs when an X-ray is incident upon thedispersing crystal, we introduce the concept of the reciprocal lattice(cf. Buerger, X-ray Crystallography, p. 107).

The reciprocal lattice of the crystal analyzer is defined as thetotality of points r* (h h h given by 1 2 3) 1 1* 2 z* "is s whereh1h2h3 are the Miller indices and (1 a 42 the reciprocal lattice vectorsrelated to the unit cell translations of the analyzing crystal a a a bythe definition 2X 113 N *f-TqC j (3) Cyclic permutation of a2 and (l3.'7 If the X-rays of wave-length A are incident upon the is designated theEwald sphere of reflection. Diifraction from a given set ofcrystallographic planes (h h h takes place in the direction s wheneverthe vector r*(h h h satisfies Equation 4; the direction of difiractionis given by In the most commonly used arrangements for X-rayspectrochemical anlysis, the detector rotates at twice the angular speedof the crystal. In reciprocal space, this means that s rotates insynchronism with the crystal,

about the origin of the reciprocal lattice, and the terminus of s movesalong a straight line which passes through the origin and at least onepoint of the reciprocal lattice.

The locus of points satisfying (4) is a sphere of radius 1/ A. It ismore convenient, however, in considering conventional spectrographicinstruments to have the sphere of reflection of unit radius, since asphere of reflection of unit radius, applicable to all wave-lengthsemanating from the specimen, can then be considered as an integral partof the instrument. This can be easily accomplished by regarding thelocus of points r=r* satisfying the equation 1=r-l-s as the unit sphereof reflection associated with central ray So.

For each ray in the cone incident on the crystal, there corresponds aunit sphere of reflection. The assemblage of these spheres, which have acommon point at the origin of reciprocal space, forms a solid shell-likefigure.

We shall designate this solid figure as the lunoid of reflection, sinceany section through it will generate a pair of lunes. The center of theEwald sphere associated with the central ray s shall be considered asthe center of the lunoid, and any point within the shell can bedescribed in terms of the values of 1x and f3, of the incident ray whoseassociated Ewald sphere passes through the point. Therefore, if areciprocal lattice point lies within the lunoid of reflection, the Lanecondition is satisfied and diffraction can take place in the direction sobtained by drawing a unit vector along the line joining the center ofthe proper Ewald sphere to the reciprocal lattice point. The diffractedrays will be recorded, however, only if they enter a detector. Becauseof the limiting apertures 7 the detector can receive only thosediffracted rays which have directions within a? and of the unit vector sassociated with the central ray s This is shown schematically in FIG. 2in two dimensions. Only those reciprocal lattice points lying within thearea ABCD will be detected. In three dimensions, the area ABCD becomes avolume in reciprocal space, which shall be designated as the detectingvolume. As the crystal is rotated, the detecting volume then sweeps outa volume in reciprocal space, and all reciprocal lattice points lyingwithin this swept-out volume will be recorded.

In general, the shape and position of the detecting vola a 5 5 thedirection s of the central ray of the ume depends in a complicated wayupon the divergences incident beam, and the angleY corresponding to theinstantaneous position of the detector. Using the concept of thedetecting volume, it is possible to ascertain under what conditionsextra reflections will be manifest, and what measures may be taken toavoid these extra reflections.

As with the intensities of normal reflections, the intensity of extrareflections when they are manifest depends markedly upon the physicaldimensions of the crystal, fluorescent source, cross-section of thedetector and linear separation of these elements, in addition to theangular divergences which determine the detecting volume, cf. Spielberg,Parrish and Lowitzsch, Spectrochim. Acta 3, 564-583 (1959).

If the divergences a and a are small, which is the usual case inconventional spectrochemical analysis systerns, extra reflections due toreciprocal lattice points in the plane of diffraction are notintercepted by the detecting volume since the width of the detectingvolume in this plane is usually sufficiently small. Thus, it can be seenin FIG. 2 that if 0: and (1 are negligibly small, the area ABCD becomesvery small.

FIG. 3a shows a cross-section through the lunoid of reflection in thelateral plane of diifraction taken for convenience at Y=0, where again01 are negligibly small, but ,8 B are not small. In this cross-section,the detecting volume is shown as a bifoliate figure. The maximumdimension of this figure projected on the line BOC is 2 (sin [Sgt-sin Asthe detector scans in the 2:1 manner, the center of the detecting volume(which corresponds to the end POlHl'. of

s) moves along the line 0A in FIG. 3b as already de scribed. Thedetecting volume, and in particular its projection onto the planecontaining 0A and ECG, will change shape somewhat as scanning proceeds;however, the length of the detecting volume parallel to BOC will notchange. Therefore, the projection of the swept-out volume on the planecontaining 0A and BC will be a rectangle of dimensions centered aboutthe line 0A. Any reciprocal lattice points that lie within thisrectangle will be detected and recorded. Strictly speaking only thosepoints lying within the trace rather than the projection of thedetecting volume will be detected and recorded. Those points lying onthe line 0A correspond to the principal planes and higher ordersthereof, whereas those points lying ofi the line 0A correspond to theextra reflections from the planes with tilted normals.

Because the occurrence of extra reflections depends upon the incidentwave-length, the spectrometer geometry, and the size and orientation ofthe reciprocal lattice cell of the monochromator crystal, themanifestation of extra reflections can be predicted when these factorsare known. Let p* be the distance from the line of reciprocal latticepoints being scanned (0A in FIG. 3b) to the closest point off the line.If

Ap* sin d-ksin fig) extra reflections will occur. (To be sure, some ofthese extra reflections may be of such weak intensity as to beundetectable.) To suppress or eliminate these extra reflections, theparameters 2*, {3 and ,6 are chosen so that Xp* sin tip-sin p* can becontrolled by appropriate choice of crystal and/or orientation of thecrystal. By choice of the crystal, we mean a crystal having as low adensity as possible of reciprocal lattice points in the directionsencompassed by the detecting volume, i.e., for the case cited, in thedirection normal to the plane of diffraction. Such a choice is possibleby considering the space group and the reciprocal lattice dimensions ofthe crystal selected. For a given crystal, since reflection from theprincipal planes will be undimensioned when the crystal is rotated aboutthe normal to the principal planes, the crystal can be oriented tomaximize the value of p*. For a given crystal, oriented for a fixed p,the inequality can be maintained by decreasing the angular divergences 8and/or B by the use of sets of parallel foils, collimating slits, ortubes. Since such collimation results in a reduction in intensity (forthe principal planes), adjustability of the collimation can be providedconditioned by the minimum value of A to be encountered in thespectrochemical analysis. Conversely, if the value of Ap is suflicintlylarge, the values of ,8 and/or 18 may be increased thereby increasingthe intensity of reflections from the principal planes withoutencountering extra reflections. FIGS. 4a, b, c and d illustrate theseprinciples. In FIGS. 4a and 4b, a quartz crystal has been used, the

principal planes (203) reflect at a d-spacing of 1.37 A. In FIGS. 40 and4d, a topaz crystal has been used, the principal planes (303) with ad-spacing of 1.36 A. All chats show pincipally the BaK spectum,\=0.330.39 A., in addition to a trace of strontium (0.8 A.). Extrareflections are seen in FIGS. 4a and 4c. The extra reflections apparentin FIG. 4a have been suppressed as shown in FIG. 4b by rotating thequartz crystal from its orientation in FIG. 4a by 90 to a neworientation. In so doing, the value of 17* has been increased from 0.06Ar to 0.41 Ar In FIGS. 4c and 4d, the suppression of extra reflections(FIG. 4d) has been accomplished by reducing the value (sin 6% sin [3%)from 0.50 to 0.10 by reduction of ,8 and B i.e., by introducingcollimation before and after the crystal. By comparing FIGS. 40 and 4d,it Will be seen that the intensity of the principal reflections issmaller for FIG. 4a than for FIG. 4c. In selecting crystals of thisd-spacing on the basis of reflectivity of principal planes, the relativeintensity between FIGS. 4b and 4c'would normally be the controllingfactor. However, it is seen that by comparing FIG. 4d with FIG. 4b, thatthe superior reflectivity of topaz is almost completely nullified. Byextension of the principles stated here, the lateral apertures used inFIG. 4b can be made larger without introducing the extra reflections andthereby the reflectivity of the quartz be made comparable or superior tothe topaz since the best value of p* for topaz (303) is less than thebest values of 12* for quartz (203).

It will thus be seen that a proper choice of crystal, orientation of thecrystal, or additional collimation, or a combination of any of thesefeatures, results in elimination or suppression of the extra reflectionswhich might lead to possible misidentification of elements in thespecimen, or materially reduce the sensitivity of the instrument. Thechoice of the particular expedient will be dictated by the choice ofcrystals available to the op erator. Thus, for a given crystal such astopaz, additional collimation may be required. If a quartz crystal isavailable, a preferred orientation will result in the suppression orelimination of the extra reflections. If other crystals are available, ajudicious selection may suflice to minimize these extra reflections. Inany event, the invention aflords a choice of expedients for suppressingor eliminating these extra reflections thereby simplifyingidentification of elements in the specimen and increasing thesensitivity of the instrument.

While We have described our invention with reference to specificembodiments, other modifications thereof will be apparent to thoseskilled in the art. Accordingly, we do not Wish to be limited to thoseembodiments since the invention is defined in the appended claims whichshould be construed as broadly as possible.

What we claim is:

1. In the method of analyzing a material for constituent elementsthereof including the steps of exposing a specimen of said material to abeam of X-rays of a wavelength which excites the fluorescent X-rayspectrum of at least one of the elements of said specimen,monochromatizing a beam of said fluorescent radiation by reflection froma surface of a reflecting crystal, and measuring the intensity of thereflected beam, the step of suppressing extra reflections from planes ofthe monochromatizing crystal whose normals are tilted with re- 6 spectto the principal diflracting planes of the crystal by making Xp* (sinBad-sin 5%) where p* is the distance from the line of reciprocal latticepoints being scanned to the closest point off the line, and ,8 and B areangles of divergence of the beam incident on and reflected by thecrystal in the lateral plane of diifraction, respectively.

2. In the method of analyzing a material for constituent elementsthereof including the steps of exposing a specimen of said material to abeam of X-rays of a wave-length which excites the fluorescent X-rayspectrum of at least one of the elements of said specimen,monochromatizing a beam of said fluorescent radiation by reflection froma surface of a reflecting crystal, and measuring the intensity of thereflected beam, the step of suppressing extra reflections from planes ofthe monochromatizing crystal Whose normals are tilted with respect tothe principal diflracting planes of the crystal by selecting a crystalsuch that where 12* is the distance from the line of reciprocal latticepoints being scanned to the closest point oflf the line, and p, and areangles of divergence of the beam incident on and reflected by thecrystal in the lateral plane of diffraction, respectively.

3. In the method of analyzing a material for constituent elementsthereof including the steps of exposing a specimen of said material to abeam of X-rays of a Wave-length Which excites the fluorescent X-rayspectrum of at least one of the elements of said specimen,

monochromatizing a beam of said fluorescent radiation by reflection froma surface of a reflecting crystal, and measuring the intensity of thereflected beam, the step of suppressing extra reflections from planes ofthe monochromatizing crystal whose normals are tilted with respect tothe principal diifracting planes of the crystal by orienting the crystalso that where p* is the distance from the line of reciprocal latticepoints being scanned to the closest point off the line, and 3 and B areangles of divergence of the beam incident on and reflected by thecrystal in the lateral plane of diffraction, respectively.

4. In the method of analyzing a material for constituent elementsthereof including the steps of exposing a specimen of said material to abeam of X-rays of a Wave-length which excites the fluorescent X-rayspectrum of at least one of the elements of said specimen,monochromatizing a beam of said fluorescent radiation by reflection froma surface of a reflecting crystal, and measuring the intensity of thereflected beam, the step of suppressing extra reflections from planes ofthe monochromatizing crystal Whose normals are tilted with respect tothe principal diffracting planes of the crystal by decreasing the anglesof divergence of the incident and reflected beams such that Ap* (sin B+sin [3 Where 12* is the distance from the line of reciprocal latticepoints being scanned to the closest point off'the line, and 18 and 8 areangles of divergence of the beam incident on and reflected by thecrystal in the lateral plane of diffraction, respectively.

5. In the method of analyzing a material for constituent elementsthereof including the steps of exposing a specimen of said material to abeam of X-rays of a wave-length which excites the fluorescent X-rayspectrum of at least one of the elements of said specimen,monochromatizing a beam of said fluorescent radiation by reflection froma surface of a reflecting crystal, and measuring the intensity of thereflected beam, the step of suppressing extra reflections from planes ofthe monochromatizing crystal whose normals are tilted with respect tothe principal difiracting planes of the crystal by decreasing at leastone of the angles of divergence of the incident and reflected beams suchthat Ap* sin 6% sin 6%) where p* is the distance from the line ofreciprocal lattice points being scanned to the closest point off theline, and 3 and {3 are angles of divergence of the beam incident on andreflected by the crystal in the lateral plane of diflfraction,respectively.

6. In the method of analyzing a material for constituent elementsthereof including the steps of exposing a specimen of said material to abeam of X-rays of a wave-length which excites the fluorescent X-rayspectrum of at least one of the elements of said specimen,monochromatizing a beam of said fluorescent radiation by reflection froma surface of a reflecting crystal, and measuring the intensity of thereflected beam, the step Ap* sin B +sin 6 is obtained where p* is thedistance from the line of reciprocal lattice points being scanned to theclosest point 05 the line, and 8 and 5 are angles of divergence of thebeam incident on and reflected by the crystal, respectively.

References Cited in the file of this patent UNITED STATES PATENTS2,386,785 Friedman Oct. 16, 1945 2,428,796 Friedman Oct. 14, 19472,449,066 Friedman Sept. 14, 1948 2,642,537 Carroll June 16, 19532,829,262 Harnacker Apr. 1. 1958 2,853,618 De Marco Sept. 23, 1958UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No.3,072,789 January 8, 1963 Joshua Ladell et al.

It is'hereby certified that error appears in the above numbered patentrequiring correction and that the said Letters Patent should read ascorrected below.

Column 2, line l6, strike out "crystal on the crystal at O is diffractedin a direction; column 3, line 15, the equation should appear as shownbelow instead of as in the patent:

line 56, strike out. "ume depends in a complicated way upon thedivergences", and insert the same after "vol" in line 53, same column 3;column 4, lines 10, 24, 44, 51, 66, column 5, line 20, column 6, lines4, 22, 42, 64, and column 8, line 8, for that portion of the equationsreading "sin sin [3 each occurrences, read Sim-B l s n 5 column 5, llne9, for

" chats snow pinci'pally" read charts show principally" column 7, line11, the equation should appear as shown below instead of as in thepatent:

hp* (sin [3 sin B Signed and sealed this 15th day of October 1963 (SEAL)kttest:

ERNEST W. SWIDER r EDWIN L. REYNOLDS \ttesting Officer ActingCommissioner of Patents

1. IN THE METHOD OF ANALYZING A MATERIAL FOR CONSTITUENT ELEMENTSTHEREOF INCLUDING THE STEPS OF EXPOSING A SPECIMEN OF SAID MATERIAL TO ABEAM OF X-RAYS OF A WAVE-LENGTH WHICH EXCITES THE FLUORESCENT X-RAYSPECTRUM OF AT LEAST ONE OF THE ELEMENTS OF SAID SPECIMEN,MONOCHROMATIZING A BEAM OF SAID FLUORESCENT RADIATION BY REFLECTION FROMA SURFACE OF A REFLECTING CRYSTAL, AND MEASURING THE INTENSITY OF THEREFLECTED BEAM, THE STEP OF SUPPRESSING EXTRA REFLECTIONS FROM PLANES OFTHE MONOCHROMATIZING CRYSTAL WHOSE NORMALS ARE TILTED WITH RESPECT TOTHE PRINCIPAL DIFFRACTING PLANES OF THE CRYSTAL BY MAKING $P*>(SIN$1/2+SIN$2/2) WHERE P* IS THE DISTANCE FROM THE LINE OF RECIPROCALLATTICE POINTS BEING SCANNED TO THE CLOSEST POINT OFF THE LINE, AND B1AND B2 ARE ANGLES OF DIVERGENCE OF THE BEAM INCIDENT ON AND REFLECTED BYTHE CRYSTAL IN THE LATERAL PLANE OF DIFFRACTION; RESPECTIVELY.